Principles of Reactor Design GAS-SOLID INTERFACE REACTIONS David M. Hurt .E I. DU
mm DE NBMOIJIW E COMPANY. INC.,
WILMXNGTON. DEL.
A method o f correlating the performance o f small-scale with large-scale reactors hos
If. R. U. (height of &r-all reaction unit) and If. C. U. (height of catalytic unit or
been deceloped. This method, limited to gas-solid interface reactions, has proved usefulf o r the rational design of plant-scale reactorsf r o m small-scale test data. Over-all reaction rates have been shown to be a function of surface reaction rates and &ffwional, or muss transfer, ratus and these component factors have been i d .;aWlly correlated with their respectively important wriables. The new wneepts of
surface reaction unit) have been introduced as measures of over-all reaction rate and surfnce reaction rate, and used in wnjunctwn with a conventional gas-film E. T. U. as a measure of moss transfer rate. New data on gas-film E. T. U. wlues, m r i n g particle sises and shapes normally used as catalysts, are presented. Data for the oxidation of sulfur dioxide on platinum catalysts are giosn io illustrate the method.
HE central problem in the development of any chemical proceae is the rational deaign of the reactor or the equip 'mat in which the chemical changes involved in the p r o m take place. In contrast to unit operations such as heat transfer, absorption, distillstion, eta., there 6as h little p r o p in developing general principlee of design for reactom. Plant-scale reaction equipment has reached a high degrea of perfection for many specisc d o n s , but in many c a m thin haa been accomplished largely by triaI-and+mr methoda on relatively large-acde equipment. On the other hand, there are many pla&cale & c & n in uw today which am,in deet, nothing more than hundreds or even thoumnd6 of d + d e reactors srranged for parallel Bow. The problem of correlating the performance of small-scale and largemale reactors is obviously more complex than for unit opewtion equipment involving physical changes only. A review of previous work on this problem will serve to illustrate the inherent di5cultiee aa well aa the general background from which the specific solution given here waa developad. WORK OF
n.
Mol- gmmted per sewnd due to ohconid renotion Molaa ammmhtiugsmr aemnd due to tlow
Heat mansntsd per swond ahsmi@aUy IV' Net best brought in per mwnd bs flow Hest gme~atedsmr swond chemicalls " Nst heat brought in per amond by mnduotion
INVESTIGATORS
Literature referenmaon this general subject are n?t numemu?. Damk6hler (4, 6, 6) made a e r a l i d mathemattcal d y s r s of this problem by the theory o%nen$od similitude: although his work does not part~cularlyadvance the art, sin a negative aewa by demonstratin and proving the herant knitations. For the nerd case pf %uid reactants in a continuous reactor, he &with the lntemlations between the differentvariables e,~ verued by th? foUoWb% fundamental laws: Newton's law o$motion, Founer's law of heat and conduction, Fick's law of ditluaion, wnseryBtion or he then d e n d five duneponk-5 w m a t i o n of en-; ters, 'ven in nomathematical tern below, wiuch must €=&Cti& equal in both large and small reactors for complete slrmlarity:
kk?% ; e.
v,
I.
5!a
Inertis
Viscolu foroe
(Reynolds number)
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 35, No. S
di9idtiea encountered in previous attempts to correlate the pmformance of re+&=. For example, DamkWer's work & that Bimilantp of o d performance for two reactors
H. R. U. to ita component psrta may be readily derived. The derivation is made for "point conditions", or for a point in the catalyst bed where the mole fraction of reacting gss is y, and for equimolar counterdi5nsion (no volume chsnge). Eliminating (dZ/dy) fromEquations 1 and 2,
rbl"
ca"paciq without change in unit reaotor di.e ia d e the number of unita in direct rati? t o . e d + ebY d capacity maease, but thia simple methd is mther ImpractId or uueoonopic in most casm.) .It fobm that mgess can be +e in tIu8 field only by breahng down over-d? d o n rates mto two or mare compnmt faatom and cormlatmg these factors individually with thev mpeative vsriablea.
in-
The general problem of principlee of resotor design has been Limited hem to gae-8olid interface reactions in continuoustype reactam. The Bolution developed for this field consists of evaluatiug over-all reaction rates an a function of m w transfer rate and surface reaction rate, and then determining the relation between these component factom and their respective vsrisbleu that will give eatiafsctory correlation for reaotors or convertera of widely Wemnt capacity. Since moat Bolid catalysts are employed 88 *ad beds of irwuhr particband their actual Burface ia d B d t to determine, we have utilized the fsmiliar H. T. U. conoept to repreeant a measure of the d B d W of the deaired performama, with reepact to both o v e r 4 performance and ita component fsctors. We have retained the ge.s-lilm H. T. U. (height of packed bed which gives a change in partial prrsaure equal to the meen driving force llarwa the gas film) an a measure of m w transfer rata; and we have introdud the new concepts of H. R. U. (height of a d o n unit or depth of catalyat bed which giveeachangeinpartialpremnre of reactant e q d to t h e m overdl drivingforce), andH. C.U. b i g h t of a catalytic unit, or surface d o n unit, of similar meaning but r e f d to surfsce reaction driving force) us measnlw of 0ver-d reaction rate and surface reaction rate,respectively. Thua the driving forces are (a, y 3 for H. R. U.,(y UJ for H. T. U.,and @, y*) for H. C. U. The equations of de6nition, in d8emntird form, foUow for these teapls:
-
-
1943
Eliminating (dZ/dy) from Equations 2 and 3,
-
For the mmpW conditions of atesdJ. &ate, unpoisoned catslyat muface, and firstorder reaction, the dation of
fix
Substituting Equation 6 in 4,
&qulpment fer Contact COnwraiOn of Gw&m Monoxide in Water Gor with Stmm to PIpducs Carbon Maxids and Eydm em at One of the Plants of E. I. du Pont de Nsmours rud &,panay, Im.
INDUSTRIAL AND ENGINEERING CHEMISTRY
823
Subatitnting F.quation 8 in 7. Ifs
-
+
KT KC
(9)
With appropriate correction factora Equation 9 is a h applicable to reactionsinvolving a change in volume or reactions reversibly poisoned by product, reactsnt, or impurity. Change in volume d e & mass transferrate by inducing gas flow in a direction normal to the solid surface and, thus, the magnitude of H?. This correction factor can, in general, be neglected without appreciable error since it lies between (1 y)/(l y), and unity for volume decrease, or between (1 y),/(l - y) and unity for volume increase. Temporary or reversible Poisoning of an active solid surface is often a factor of major importance in determinii o d reaction rates. The noncumulative poisoning of a solid catalyst by a gaaeoua impurity is fairly well known,but the equally important and similar self-poisoning by a reactsnt or a product ia not 80 evident, although ita &ect muat like wiae be evaluated before correlation of o v e r 4 prformance for diBerent conditions c8n be expected. When the poisoning agent is a product, a reactant, or an impurity present in approximately constgnt concentration, the &e& may be treated aa nteady&ta conditions. Although the exact mechanism of poisoning is not alwsys horn, its magnitude can be evaluated most conveniently in terms of the fraction of total catalyst d a c e not poisoned. MOUE unpublishea work of the writer showed that this fractionis represented by the d i m e n a i h factor 1/11 kdpJ1 whm, for the given muface, k, varies with tempersture only. Thus, the value of € for I . poisoned d o n s is given by1:
-
-
+
HP
-
11
+ h@.)l(& + a c )
(10)
The above development therefore is applicable to true ht-order reactions, p~sudob h r d e r mtions, or reactions of 110 definite order which may be ckaed aa -do 5nb order reactionspoisoned by a product or reactant. Further-
more, it may be used for second-order reactions without apprecisble error when one reactant is almp used in large It cavern, there.fore, the majority of the reactions enaountered in practice.
-.
I
th.C0rr-t form d Eglution 10
BMd 011 pluw theQmthlrmo*.
-
should b 8.
(1
+ hn1'8r + (1 + L W E c
-
"htni muld ba.omab.tla thu,w . n dmuld N S with the f r ? m t h d the nrfsw pisonad rad with th. nkths rnunitlldea of the pl elm tblolrnr rad t h e d i . m a r ofFm *mplhiW, we hsw lued ths form intbetext.bon. B m thi.-ew&on b y been& both i.
rrmuting
d
4
e
Run No.
MmvdW..&
T hy~pollot. &ml.JnrPwl Pvtw d Inlet kir
luau extent.
-* -,
dBd
aa.'as (1?id
18.26
.h.
7 806
6
(hr.l~..ft.-don)
4
Ty~pnwe.
~ a r m S P c 8 .w
M.rad &d*
minm tlM thw i n t m d d .mud out to
0.0347 0.0117
of .nta .t .wfsw *a€....tm.
08.80
18.88
1a.s
18.46
... ...
AV. 1.14
.m
1 ~~~~
1.76 1.14 1.W a71
524
1,s
... ...
1.48 ~~~~
... Bpo
To codder the individual correlation of E.T. U.,H. C. U., and k, with their rmpectively important operating variables, the method used is to net up the most probable relations, aa b a d upon speoi6c knowledge,analogy. or deduction, and then test these assumptions by means of existing performanoe data on reactors covering a wide range in capacity. 8peci6&, the initidly m m e d relations SIW as follows: E. T. U. is inde &t of the a eific reaction or type of catalyst, is p r a c t i d i n d p d e n t of&rnperature and p m , but mnes with flow conditmons M defined bv RevnoIda number. ............................. with shape and sisa factam of the aolidba;t~cles,and wjth physicd propertiesof the gss mrrhve M defined by come function of the dimensionless p u p b/pD.). Xc for the y x f i c resctbn and the ahape, E. C. U. is h,and type o z t a l y s t , ia in ependent of Reynolds number, vmes dirmtlv with m velacitv. is indeuendent of n m . but vm% wiaely &htempat&. 'fic reaction and t ' t h in y i f i c for the caM=indepen snt of RBynol%%~~ber, varies w i t x ; ! pat-, and ia independent of total p m when the poison concentration is expressed as partial preaaure in atmospheres. DETERMINATION OF GAS-PILM
In the application of this method of correlating test data on reactors, it waa necmary to determine the valuea of H. T.U. independently before values for H. C. U. could be cnlculated, sinoe any one specific test giw only a value for the overdl d o n rata under those conditions. The only data available for transfer rates to psoked beds were those of Ahlberg (0on watar vapor absorption by silica gel particlea and thw of Fumss ( 4 9 ) on heat transfer to packed beds. These data covered only a m w range of particle size and ms8~ velocities; moreover, there was a poseibility of appreciable reeistsnces within the mlid 80 that the over-all transfer rates would not give true g a s h H. T. U. values. The underaxperimental -mt of ~ 6 l H m .T. U. taken for the various sizes and shapes of solid particles normally used a6 catalyEt3. Various types of systeme were investigated to datermine the simpleat and moet accurate system for menuwing gas 6lm E.T. U. The general method was limited to steadystste conditions in all CBBBS, since this permittad the direct evsluation of the multa and eliminated the n e t y of resorting to Elchumaan's involved method (11) of evaluating unsteedy-etste data. tried m:sdsorption of water vapor The #c from mokt air by silica gel particlea, adsorption of water vapor from moist air by particles coated with phosphorus pentoxide, adiabatic humidi6cation of air by wetted particlea (meamring both heat and m988 transfer rates), evaporation
10
11
8 6%
9 11.90
88s
206
m.80 14.70 is.m
m.80 14.06
n 00 n:n
n.06 14.06
... ... ...
... ...
....
... ... ...
i 3
i:h
16.47
i:k
1.w)
1.67
18.w 16.a
1.80
l..6T
...
... ...
'id0
'.' 8(0
...
E. T. U.
1.09 1.81
... ...
... a40
;kg ...
... ... i:&s
0.96
1.16
... ... ...
146
ia aar
....
13.~0 18.40
....
O.o(H8 0.0138
0.01€4
0.01w
.... .... ....
a m
0.9s 1.36
146
INDUSTRIAL A N D BNGINEBRING CHEMISTRY
18 102
~ . 7 8 12.81 12.18 13.m
... ...
14 716 26.61 14.70 18.80 16.87
16 716
%.as
14.30
18.80 16.07
...
... ...
.O.BO
i k 1.m
1.6a
1.07
1.67.
...
i:i6
... ...
...72
....
...
... ... ... Mb
... ...
1.a~ 1.60
.. .... 1
VoL 3S, No, 5
of naphthalene into air from naphthaleneparticles, and emporation of naphthalene into hydrogen from naphthalene particles. In dl c a m the beds of solid particles were contained in m a l l cylindrical towem with a wire screen sup port for the packed d o n . The tower diameter employed was not leas than ten particle diameteta in any case, so as to minimise any "wall edieds". The gas flows were measured hy calibrated shsrpedge orifices. The p a c W bed depth was regulsted to keep the change in gas composition in the range from about 50 to 80 per cent a p proach to equilibrium; thus the magnification of any small errom in the meat+ w e n t of exit gaa or equilibrium compoeition was prevented. The m e size and shape of particles ("9 inch diameter x a/8 inch thick, cylindrid) were maintained for the various a)% terns investigated, and the preferred method only (evaporation of naphthalene into air) was utilized for the other siees and shapes subeequently measured. The 6rat system investigated was the Filum 1 (Above). Emt and MW Tmqfer Rote beG4s S c ~ ~ m s and Pncksd Bsds of 'fa X '1s Inch Cylindriml P a r t i c k direct absorption of water vapor from moist air on silica gel particles. In an F i ~ ~ rI m(Below). Moa. Tmnsfer R a t e betwean G a S m r u ud attempt to ohbin steady-state conPockal Bed. of V&Ua Particb s i w s and shape8 ditions, the time of the runa was limited to 2 to 4 minute 80 that the equilibrium partial p m of water vapor from the gel would still be tubes packed with phosphorus pentoxide. Inlet and exit negligible at the end of the m. The water contenta of the inlet and exit air were determined by continuous eampling gas temperatures were taken, and heat transfer rate were and analyaia, and the weight i n c m of the gel determined calculated as a cheek againat m888 transfer rata. AU measurements were made under stesdJ.-Btate conditio-. as a material balance check. The results were repmducible Steady &ate (to the nesrest 0.1' C.) was reached.in &ut but showed an unexpectdy high E. T. U. of 10 inches for 8 mass relocity of 600 [or HT/oI/pD.)'f* = 13.8 inches for 5 minute with this system and Lasted about 5 to 20 minute D&/p 425,with particles a/a inch in diameter X 8 / ~inch, (depending on gas flow rate), at which time the surface of the and a bed 3.3 i n c h in diameter X 2 inches]. This indicated pallets started to dry. This method gave H. T. U. d u e s that a major Werence between equilibrium vapor pressure somewhat lower than the preceding method, and these values are believed to be the true gasfilm E. T. U. with a probable and interface vapor p m must have developed during r(ccuacy of about *IO per cent. The maea transfer and these short runa. In an attempt to eliminate the " d i d film" &e& encounb heat tramfer rata as obtained check cloeely when correlated ered in adsorbing water on silica gel, the silica gel particles by the method of Chilton and Colburn (J), which would were coated with a layer of phoephorus pentoxide, and mass not be expected if there were any appreciable e m r in this transfer rate were measured by the m e method as for the method of determining the true d a c e temperature and silica gel. In these rune the maximum time for a m wad surface vapor preseure. The experimental data are summarine3 in Table I and correlated in Figure 1. such that the total water adsorbed (or reacted) was only a fraction of ita stoichiometric eqhivdent to the phospborus The above method was aatie.fadory for a somewhat limited range of gas velocities only, since at high velocities M y pentdde present. This system gave an H. T. U. value of &ate conditions Lasted too short a t i e for accurate h t s , and 2.5 inch- at a msae velocity of 600 [or R./b/p D,)% = 3.5 inches for D&/p 425,with particles '/a inch in diameter X at low velocities adiabatic conditio- could not be main'/s inch, and a bed 3.3 inches in diameter X 2 inches]; while tained. Therefore H. T. U. values for the total velocity of the expected order of magnitude, this value still left some range desired were determined by meamring the evaporation doubt as to ita exact accuracy as a measure of the true gsk rate of solid naphthalene particles into air or into hydrogen film H. T. U. At room temperatnaphthalene has such a low partial Adiabatic hnmidfication, where the heat of evaporation is p m that the cooling atiect of evaporation is negligible supplied by the gas stream, was next investigated as a megll~ as compared to the heating Bfiect of the gas stream, and thus of eliminating the solid 6bn atiect. Partially dried air w u the surface temperature of the naphthslene (and ita conaequent vapor pressure) could be accurately determined, since passed over silica gel pellets wetted with water. The surface it could vary less than 0.1' C. from the gas stream temtemperature of the wetted peUeta WBB checked,by he-whe thermocouplesembedded in two pelleta placed in the top and perature. In this method the naphthalene vapor concentrs, bottom layeta of the packed bed, and the inlet and exit water tion in the exit gas was not m d directly but was calmpor concentrations were meaeured by sampling through culated from the gas flow rate, time of m, and loas in weight
-
-
&Y#
1943
INDUSTRIAL AND ENGINEERING CHEMISTRY
SaS
16 17 UI
19 10
'
ern
468 a26 81
ai
40.4 ai 7
22
4.8
18 a4 25 28 a7 28
466 a26 81 40 4 21.7
a9 80 31
455
a2
qs'% " ET
M.d. velooity
Lb./(Er.\ (Err. Ft.)
Run Ne.
945
945
am
I 1
2 4 6 10 14
I L I I
I I 1
M '
10
2"
I
4
I 1
10
1
1
1
6
ia
a
1
2 3
I
a
I
3 6
735 460 226 81 40.4 81.7
1 1 1
38 3s
466 226
I I
40 41
318 193
1
0.80 0.80
a
10
I6
a
3 3
4
noha
-
*/a X */# Inoh Cglindrical Putiolrs. Ai, D, 0.38 lnah 26.3 0.153 0.040 0.168 0.270 26.6 0.176 0.048 0.171 0.880 aa.9 0.159 0.069 0.176 0.408 27.5 0.137 0.088 0.184 0.W 27.8 0.116 0.101 0.187 0.758 25.1 0.108 0.124 0.181 1.06 VI X Inoh Cylindrical Putiala, Hydrogan. D p 0.38 Inoh 27.0 0,169 0.116 0.175 1.11 Vu X Vu Inoh Cylindriod Putiolaa. Air* D , 0.17 Inoh 27.8 0.a.w 0.090 0.186' 0.057 a7.4 0.lSS 0.102 0.182 0.826 0.a~ 0.118 0.124 0.936 27.6 98.4 0.137 0.143 0.193 1.88 28.6 0.130 0.162 0.196 i.7a 29.0 0.096 0.182 o.aw 8.11 8 to 4 M a h IrrPutid-, Ai, DP 0.22 Inoh 26.5 0.8ro 0.084 0.170 0.675 27.0 0.188 0.108 0.175 0.888 27.2 O.le4 0.117 0.179 1.07 4 to 6 b k h frrsrul.r Putidea. Air. De 0.10 Inoh 27.4 0.361 0.120 0.182 1.07 a7.4 o.asi o.iaa 0.182 1.17 27.4 0.188 0.135 0.182 1.3s 25.0 0.164 0.169 0.188 1.82 28.0 0.186 0.168 0.189 8.17 a8.o 0.117 0.178 0.189 2.86 6 ta 8 M a h Irrotulu Putiele, Air, D. 0.11 lnoh 29.0 0.580 0.164 0.Ml 1.43 29.0 0.221 0.1w o.mi 1.73 8 to 10 Mah InamIar Partiela. Am, D. 0.08 I d 28.6 0.288 0.148 0.196 1.40 28.8 0.240 0.152 0.188 . 1.48
of naphthalene particles. For thin purpose a special tower of low gram weight made of thin-gage aluminum t n b i i was used so that the loss in weight of the packed bed of naphthalene particles could be accurataly determined without muoval from the tower. Thia method w88 used in extending the meaauramenta to the variwe sizes and shapee of particlee normally d as c~talyste. The & and shapes 0 0 d ww '/a X '/a inch and '/B X '/,, inch cylindrical particles and irragular broken d d s of the following &a ranges: 3 to 4 meah, 4 to 6 meah, 8 to 8 mesh, and 8 to 10 meah. The experimental data are aummmkl in Table I1 and &own graphically in Figurea 1 and 2. For the m e &?aand shape of solid particles, data for the various systems m d were comlated by plotting H&/fl.)'/~ for roam trader, or H./(cp/k)'/a for heat transfer againat the modified ReynolaS number D,G//.t. For &%rent &a particles of similar shape no eatMactory c o m b tion of the data into a single curve could ha obtained. The data are, accordingly, p m n t e d as sepsrste curves for each eke and shape inveatigated. The dopea of them c u m in the turbulent and Visoous regions do not mer so widely an do the curve of pressure dmp for flow through granular solids (#), where the dope of the friction fado~&ynolaS number plot is -1 below a value of about 40, and about -0.2 above thin value. The dative positions of the curve show that H. T. U. decre9ses, in general, as particle diameter derreaaea, but that this &ect is rliminiahin.rapidly at the lowest values of D. employed.
-
. 3.70 8.03 a.45
-
1.50
a.w
670 324
1.64 1.33
180
0.67
0.72 0.52
s7.a 28.5 15.8
0.80
0.36
7.c
1.68 1.21 1.07 0.76
0.88
0.46
0.245
1.32 0.86
0.m
0.58 0.41 0.815
300 146 72 28.8 12.8
-
0.58
-
0.935
0.80 0.61 0.61
386 180 94
aar
-
1.m
i.ia
6.9
0.836
0,Sl
0.855
0.466
0.46
0.36
0.30 0.25 0.10
0.70 0.58
0.38 0.316
96
0.67
0.31
46
0.74 0.66
0.W
0.64
0.m
139 08.6 24,s 12.2
6.6
47
18.9
pmmsea for which diciently detailed data on d e and largemale reactom are available. Previous unpublished work of the writer covering an extensive investigation of the reaction rates for oxidation of eulfur dioxide over platinum cstalysta for equipment sises ranging from laboratory scale up to fnU plant scale has been thus correlated. Thia reaction is reversibly poisoned by the reaction product sulfur trioxide, so that for this case:
to
both d
Ea
-
(1
+ hPw.)(Hr + Hc)
(11)
Values of b w. temperature for two typea of platinum catalyst for this reaction are shown in Figum 3, and H . is plotted sgainst temperature for the m e cstalysta in Figwe 4. Values of H. T. U. are aa shown in Figure 2, the value of ol/pD.)*~~ being 1.18 for sulfur dioxideair. H. C. U. Varies Taem III. R e u r n I m m c n or Maae 'Ihwsm~AND S U R F AR~E A ~ OR Nam m n AVERAQE OPEUAllNQ CONDlTIONE
WRR&IATXON OF EXISTING DATA
In drder to demonstrate their application and aa a general test of their validity, the metbods developed m r e applied 526
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
VoL 3% No. 3
I N D U ST H I A L R B A C T I directly with maes velocity, and since the valuca Shown in the plot m spacific for f3 = 6OOpoun&/(squsre foot)(hour), H. C. U. valuea for other m a s velocitim equal H. C. U. (from plot) X f3/800.
200
TNPERATURE -'C. 400 450 500 550 600
350
too
i
actual with calculated results then indicated the accuracy of the correlation. A number of other gss-solid interface reactions have been reviewed from the Btsnapoint of Bimilarly breaking down the over4 paction rates to permit the correlation of dand lmge-ede data. The approximate r~lativeimportance of maea bander rate and surfsce reaction rate for variow aMmercial reactions under average planeSeale conditions is ehown in Table 111. No major discrepsncies between amall- and kge-sde d t s w h found when analyzed by thin method, although the data in most (18888 were much ken complete than for d w dioxide oxidation.
50
DISCUSSfON
k 30 '20 I
a - IO
S 3 '17
H AT R S
16
I5 1.4 13 I / T X IO4
12
It
',t.
In all 9f this work the conditio- messary for attainment of thermodynamic rdmilarityhave be en intention ally^^ for the following reawns. Laboratory or d d e teats are ilwrently isothermal, w h large-ede t83t8.m i d m y t l y sdiabstia or at le& n o & t h d . W m complete thermodynamic rdmilarity, although perhp k b l e , is in general impractical of attainment or leads to ec~nomicallyuafeaebb typee of equipment. We themfore preferred to c o d a t e surface reaction'rates with the nonindependent variable, temmture. This necBBBitateB the UBe of stepwise dculationn in evaluating performance ,* obtsined under no&tbmd conditians or, WnBrSBIJT, when calculating performance under d b i m i h n & W conditio-.
This correlation covers the complete range from laboratory up to full plant scale reaults, or for catdyat volume from about 100 ml. up to about 100 cubic feet, mgss velocities from about 35 to 800 pun&/(square foot)(hour), and inlet gas compositiona from 1 to 10 per cant sulfur dioxide. It is estimated that the acmvsoy is within about 20 per cent, or only slightls less than the average reproducibility of these catslyate.
The plots of kt and H. C. U. (in conjunction with appm priate H. T. U. valum) completely d e h e the catslyst performanca under any conditions. Plots for two repmsntative platinum catslyate (A and B) are included to illustrate the equal slopes of the draighbline plots obtsined by using logm i p d coordinates. From the dope of the H. C. U. plots the calculated activation energy for this reaction is 26,800 gram-calonca per gram mole. Similarly, from the slope of the k, plots the heat of adsorption for sulfur trioxide on platinum black is estimated as 12,100 gram-doriea per gram mole. The method of correlatii spedic test data ranging from laboratoryde to plant teste by theae plots w88 as follows: The k, and H. C. U. plots were drawn from points calculated from laboratory+cale isothermal tasts. This repuired two teste, msde under essentially similar conditions except for Merent average sulfur trioxide concenbations, at each temperatm. Obviously any one test givea only a value for H. R.U.,with three component parts, under those conditions. But aince H. T. U. is independently known, two tests permit the evaluation of k, and H. C. U. by the method of simultsneous equations. T h w plots were then uaed to drmlate the performance of pilot or full-scale plant under adiabatic conditions. This was done by a stepwise calculation with a d e n t number of Bteps to reduce the error, owing to sasumption of imthermal conditiins and conatant poimninp fsdor in each Btep, to negligible amount. Comparison of May, 1w
Figures 1,3, and 4 Show that all three component factors have an important eEect on the over-aU reaction rate for the oxidation of sulfur dioxide on platinum. However, their relative magnitude will vary gre!itly with Bpecilic conditions as to maea velocity, temperature, and partial preseure of
INDUBTRIAL AND ENGINEERING CHEMISTRY
sa7
I
sulfur trioxide. Thus for catslyst B, with a msss velocity of 600 pounds/(bour)(square foot), the height of a mass trsnsfer unit would remain constant at 2.0 inches while the height of a catslytic Unit would vary from 0.22 inch at 575" C. to 33 at 375", and the sulfur trioxide poieoning factor would wry from 1.04 (for0.01 atmosphere d f u r trioxide and 575' C.) to 5.3 (for 0.1 atmosphere and 375'). For thesame cat9.lsst but a mas velocity of 50 (comparable to small-scale teat conditions) H. would be conatant at 0.95 inch, € would Io wry from 0.02 inch at 676' C. to 2.76 at 375O, while the poieoning factor would be the same aa for the higller flow. At high t e m p e r a h , thedore, the o v e d reaction rate is largely controlled by maes transfer rate, while at low temperatures surface d o n rate is mast important when sulfur trioxide p m is low, or sulfur trioxide poieoning in mast important when d f u r trioxide pressure is high. Table III &tows that mass transfer rate is an important contributing factor (and in some caees largely controlling) for the o v e d d o n rate for many industrial reaction%. The small mount of published performance data on specific catalynt8 would scarcely confirm this conclusion. However, in general, the more active the catdpt, the gmter the relative importance of mB(y1 transfer to overall d o n rate,and few if any chemical wmpanies publish performance data for their most active cataIynt8. This work should End ite major application in connection with the development of new producta or pmcemes, in that it should permit more accurate deaign of the initial pilotplant equipment and full-ecale equipment. It slso permita quantitative evaluation of the factors governing economic type or Bise of equipment from small-ecale data, and thus development work can be concentrated on the specific type of equipment which in most faasible economidy for the specific reaction. For existing prooesses the m e methods can be used for determining the economic jnstiiication for changing type or size of existing convertem. In general, the work to date indicates that Iahoratory-scale teat data made under approxjmately isothermal conditions, when correctly interpreted, give a more accurate indication of plankcale performance than can be obtained from semiworke-scale tests, where accurate control and measurement of conditions are more dj5cult. The various factors aBecting optimum type and size of resotor from the economic standpoint are 80 numerous, and the relative magnitude of these factors varies 80 widely for a e r e n t reactions, that any generalisationsattempted would be limited in applicability. However, the general type of equipment to be preferred for any specisc reaction can often be p d c t e d from general knowledge or experience. For example, reactions with nnfavorahle equilibrium constants require either recycling or ever4 reactors in aeries with intermediate removal of product in order to secure sat.& fadory over-all yield; reactions with sstisfactory equilibrium constmta hut, high reaction heata require continuous or intermittent removal of heat or dilution with an excess of inerta or one reactant; while those with favorable equilibrium values and low reaction hwta may be sstisfactorily camed out in SinglRStage sdisbstic systems. Therefore, for some reactions the genersl type of quip ment necessary can he determined by inspection. However, in many cases the choice is not obvious and must be based on economic compsrisons. For example, in the oxidation of sulfur dioxide, it is evident that ediibatic convert8r6, which are cheapest to construct, are le& e6icient from etandpoint of catslwt performance; on .the other hand, i n k 1 heat-exchaoge t y p deaigned for decreasing temperaturea in direction of gas flow, or loweat catalyst temperatures at the exit end, will he most expanaive but mast e5cient. Converters giving approximat& ieothermsl con5%
ditioos come somewhere between theee two extremes. Thus qualitative knowled~in not sufficient to determine the reepective over-all merita, and it in necessary to u ~ quantie tative data of the type shown. From them the optimum performance and ~peciiicsize and cost can be accurately eetimated for each geum1 converter type, and the ultimate choice an to equipment can be bawl on over-all economic cousiderations. The eame general p m d u r a applies to pilotplant deaign aa for full-scale plant design. The preferred t y p of fullscale equipment should be determined hefore the pilot plant is de6igned 80 that the pilot plant may more nearly resemble sealeddown plant equipment than scaled-up laboratory equipment. The major purpoee of thii work wan to develop means for reducing or eliminating trial-and-error development methods with act& equipment. It is believed that this can be 80complished through the quantitative methoda developed here for predicting performance of a given type and Bise of reactor. It in not implied that pilotplant d e equipment is to he outmoded, but rather that the function of the pilot plant may be con6ned to con6rmation of resation rates, confirmation of mat&& of construction, and evaluation of economic catalyst life under commercial o p m t i q conditions. ACKNOWLBDGMEW
The author wishes to expm his appreciation to T. E. Chilton, C. M. Coopa, end W. H. McAdams for their helpful mggeationa and criticisms concerning this work.
c
h
D, f3
Hc
----
cific heat at oonstant pressure, P. c. u./flb.)(' C.) % & i t , 4.ftb. +ICI +1cleLeter;rt superfieid msar velocity, v&city, Ib./(hr.)(sq. ft.) ft.) heght- oc c+&ti c~alalytrc c (or surface reaction) reactron) unit,
-------lb I p;, pl p.
i.+?miLd values
of p
-
-
Ap,
partial p m of poiaoni component, atm. mean partial pressure dnving force across ged
T
absoluie temperature, OK.
;
h, It & y yc y*
(1
NOMENCLATUHB
p P
-
61m. atm.
temperatq O C . terminal values of f mean temperature driving force acmss gea 6lm, O C. mole fraction of reacting gss in gas stream mole fraction of reacting gss at -lid mterfaca equilibrium vdue of y at surface tempsratnre of u) and (1 yr) Bd bed, in.
2VkwEiiY K.hr. (ft.) density, b./(mA.
-
)
LITERATWRL CITED
Ahiberg, J. E.,b. ENa. Cam.. 51. WS8-92 (1989). Chilton. T. H., .nd Colbum. A. P., M . ,23,918-19 (1931). M.. 26, 1183-7 (1934). Dsmkbhlesr, GI.. in Eucken snd J.Lob's "Der Chemie-hiCFmiau". Vd. 111, Part 1, pp. 46868.Isiplig. Akndemhb Vetgwellschsft. 1987.
(mas). D - M M ~ , GI.. z.~bktro~unr.. 42. IW.. 43, 1-13 (1980. EdgmorthJohmtom. R.. Tmnt. I&. Gwm. Bnm.. (London). 17, 1 W 8 (1939). hunaa, C. C., Im. ENQ.clm., 22, 26-31 (1980). Funsa.C. C.. !?+am.Am.I d . O h .Ewm..Z4,142-86 (1830). L.upichler, F. GI.. b. ENQ.Carm., SO. 67846 (1838). Elohumann, T. E. W.,J . Fmnkl
